The realization space is
  [1   x1 + x2 - 1   1   0            x2         x1 + x2 - 1   1   0                     0    1                      x1*x2 - x1 - x2 + 1]
  [1         x1*x2   0   1   x1 + x2 - 1   x1^2 + x1*x2 - x1   1   0   x1*x2 - x1 - x2 + 1   x1                                        0]
  [1         x1*x2   0   0            x2               x1*x2   0   1                 x1*x2   x2   -x1^2*x2 + x1*x2^2 - x1*x2 - x2^2 + x2]
in the multivariate polynomial ring in 2 variables over ZZ
avoiding the zero loci of the polynomials
RingElem[x1*x2 - x2^2 + 2*x2 - 1, x1, x1 - x2 + 1, x1 + x2 - 1, x2, x1^2 - x1*x2 + x1 + x2 - 1, x2 - 1, x1 - 1, x1^3 - x1*x2^2 + 2*x1*x2 - x1 + x2^2 - 2*x2 + 1, x1^3*x2 + x1^2*x2 - x1^2 - x1*x2^3 + 3*x1*x2^2 - 3*x1*x2 + x1 + x2^3 - 2*x2^2 + x2, x1^3 + x1^2*x2 - x1^2 - x1*x2^2 + 2*x1*x2 - x1 + x2^2 - 2*x2 + 1, x1^2*x2 - x1*x2^2 + 2*x1*x2 - x1 + x2^2 - 2*x2 + 1, x1^2 - x1*x2^2 + 3*x1*x2 - 2*x1 + x2^2 - 2*x2 + 1, x1 - x2, x1^2*x2 + x1*x2 - x1 + x2^2 - 2*x2 + 1, x1^2 + x2 - 1, x1 - x2^2 + 2*x2 - 1]